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Analytical Theory of Biological Populations (The Springer Series on Demographic Methods and Population Analysis)
(In the 50 years that have passed since Alfred Latka's dea...)
In the 50 years that have passed since Alfred Latka's death in 1949 his position as the father of mathematical demography has been secure. With his first demographic papers in 1907 and 1911 (the latter co authored with F. R. Sharpe) he laid the foundations for stable population theory, and over the next decades both largely completed it and found convenient mathematical approximations that gave it practical applica tions. Since his time, the field has moved in several directions he did not foresee, but in the main it is still his. Despite Latka's stature, however, the reader still needs to hunt through the old journals to locate his principal works. As yet no exten sive collections of his papers are in print, and for his part he never as sembled his contributions into a single volume in English. He did so in French, in the two part Theorie Analytique des Associations Biologiques (1934, 1939). Drawing on his Elements of Physical Biology (1925) and most of his mathematical papers, Latka offered French readers insights into his biological thought and a concise and mathematically accessible summary of what he called recent contributions in demographic analy sis. We would be accurate in also calling it Latka's contributions in demographic analysis.
(Formerly published as Elements of Physical Biology, this ...)
Formerly published as Elements of Physical Biology, this classic is the first major attempt to apply modern mathematics to the problems of phylogeny, ontology, ecology, physiology, endocrinology, psychology...
Alfred James Lotka was an American mathematician and statistician. He served as a supervisor of mathematical research at Metropolitan Life Insurance Company, New York City from 1924 to 1947.
Background
Alfred James Lotka was born on March 2, 1880 in Lemberg, Austria-Hungary (now Lviv, Ukraine). He was one of at least two children of Jacques Lotka and Marie (Doebely) Lotka. Both parents were American citizens who had spent most of their lives in Europe. They were, according to Lotka's own account, missionaries, possibly of the Moravian denomination. He spent his boyhood in France.
Education
Lotka received his higher education in England, obtaining the Bachelor of Science degree from Birmingham University in 1901. Already interested in physics, chemistry, and biology (especially self-renewing processes), he spent the graduate year at the University of Leipzig, where he developed his concept of the mathematical theory of evolution. Later he continued his graduate study in physics at Cornell University, which awarded him the Master of Arts degree in 1909; three years later he obtained the Doctor of Science degree from Birmingham University.
Career
Lotka arrived to the United States in 1902 and obtained employment as an assistant chemist at the General Chemical Company, where he remained until 1908. Later he worked as an examiner at the U. S. Patent Office (1909) and as assistant physicist at the U. S. Bureau of Standards (1909 - 1911). After serving three years as editor of the Scientific American Supplement, he returned to General Chemical (1914 - 1919). Throughout these years Lotka's active mind ranged over a broad field of investigation; indeed, the breadth of his interests was comparable to that of the seventeenth-century natural philosophers. A quiet, learned man who expressed himself with equal facility in English, French, and German, he wrote numerous articles for both scholarly and popular journals. His interest in population studies, in fact, emerged as an aspect of his broader concern with physical and especially bio-physical processes, including the evolution of organisms.
Lotka was a close student of such scientists as Albert Einstein, Hendrick Lorentz, and J. J. Thompson. In "A New Conception of the Universe, " published in Harper's Monthly in April 1920, Lotka presented perhaps the most intelligible exposition of the theory of relativity ever offered to laymen and suggested--two decades before the atomic bomb--the enormous potential inherent in knowledge about the atom. In 1922 Lotka began two years in residence at the Johns Hopkins University, pursuing independent research and codifying his earlier studies into a book, Elements of Physical Biology (1925).
Despite the range of Lotka's interests, his enduring reputation rests chiefly on his contributions to demography. Central to his demographic studies and subsequent mathematical demography was the analysis of the structure of a stable population, a hypothetical population formed by constant age-specific birth and death rates and unaffected by migration. This concept had been approached but never fully developed in previous studies. As early as 1760, Leonard Euler, the Swiss mathematician, had formulated the age distribution of a population with a constant schedule of mortality at successive ages and a constant ratio of births in successive years. Lotka's three earliest scientific contributions in 1907 included two significant articles on apparently unrelated topics: "Relation between Birth Rates and Death Rates" and "Studies on the Mode of Growth of Material Aggregates" (respectively in Science and the American Journal of Science). Their linkage in his approach to science is shown in the concluding sentence of the second article: "We have illustrated a statistical method which is sufficiently general in its application to comprise such widely different cases as that of the growth of a population under certain conditions, on the one hand, and that of a simple chemical reaction on the other. "
"A Problem in Age Distribution, " coauthored with Francis R. Sharpe, which appeared in Philosophical Magazine in 1911, showed that a closed population, submitted to fixed female (or male) rates of mortality and fertility and a constant sex ratio at birth, would develop a stable age distribution with a characteristic rate of increase. Lotka's concentration on demography dates from 1924, when he was appointed supervisor of mathematical research in the statistical bureau of the Metropolitan Life Insurance Company. He remained with the company until his retirement in 1947, becoming general supervisor of the statistical bureau in 1933.
Lotka's contribution to demography first attracted wide attention in the article "On the True Rate of Natural Increase" (coauthored with Louis I. Dublin), which appeared in the Journal of the American Statistical Association in September 1925. Written just after the United States opted for a restrictive immigration policy, the article, based on data for 1920, demonstrated that the "crude" official rate of natural increase of the population, calculated at 10. 7 per 1, 000, was misleading and that the "true, " or "intrinsic, " rate was only 5. 2. It was shown that the crude rate was distorted by the age distribution of the American population, at that time with a relatively high proportion of adults in the twenty-to-forty-five age group, the central reproductive period. The authors predicted the eventual stabilization of the declining American birthrate and a decline in the rate of natural increase. Dublin later recalled that as a result of this article, "Malthusian fears of overpopulation gave way to alarm that the Western populations were headed for great declines in numbers".
The stable population theory developed by Lotka proved to be a key instrument of demographic research. The three major characteristics of a population--age distribution, mortality schedule, and fertility--are so interrelated that any one can (disregarding the effects of migration) be mathematically derived from knowledge of the other two. This is especially useful in the investigation of populations with incomplete or erroneous data. It proved that the major determinant of population's age distribution is the previous level of fertility rather than mortality (as earlier demographers believed). Although subsequent scholarship has pointed out certain limitations of the theory as initially presented, it has illuminated a host of demographic questions.
Lotka also made many specific contributions to various aspects of population study. At Metropolitan Life, Lotka benefited from his association with Dublin, whose socially sophisticated, outgoing personality differed sharply from his own. However, each tended to minimize the contribution of the other to their collaborative efforts on several articles and three important books: The Money Value of a Man (1930), Length of Life (1936), and Twenty-Five Years of Health Progress (1937). Unfortunately, he became involved in a long, sterile controversy with R. R. Kuczynski. In line with his central interest, Lotka's work in demography was directed mainly to the analysis of what he called "necessary relations, " the relations inherent in the physical structure of all organisms. This philosophical concept found expression in his Analyse demographique avec application particuliere a l'espece humaine, published in France in 1939.
Lotka belonged to several professional societies, including the Institute of Mathematical Statistics and the American Public Health Association. He was president of the Population Association of America (1938 - 1939) and the American Statistical Association (1942) and vice-president of the International Union for the Study of Population (1948 - 1949).
Personality
Lotka was generally gracious and had a lively, although wry, sense of humor. He lacked interest in organizational activities and rarely participated actively in scientific assemblies.
Connections
Lotka was a bachelor until his fifty-fifth year. He married Romola Beattie on January 5, 1935. They had no children.